You might be tempted to say, " Of course they don't! how can fish feel thirsty when they are practically surrounded by water all the time?". Or you start thinking about how saltwater makes you thirsty and maybe the same thing happens to a fish.
Although it is impossible to know exactly how a non-human animal truly feels it is possible to make a pretty good guess.
What is thirst?
In the most basic terms, it is the urge to drink water. Humans show this desire in varying degrees (you can be just a little thirsty or I-can-drink-the-whole-bottle thirsty). This desire to drink water is our way of making sure that a healthy balance of water and salts is maintained inside our body.
Not only humans but all animals living on the land are faced by the threat of dehydration, and therefore feel thirsty when their body needs water.
However, Regardless of their thirst drive (or lack thereof), all creatures need hydration to stay alive. They regulate water balance through a process called osmoregulation, which is common to many animals, including humans.
Freshwater Vs Saltwater
The type of water a fish lives in is very important in determining how the fish maintains a salt-water balance in its body.
The blood and tissues of freshwater fishes have a higher concentration of salts than the water surrounding them. Therefore if they drink too much water they run a risk of diluting their blood and tissues. This is why Freshwater fishes don't actively drink water through their mouths.
Freshwater fishes absorb water through their skin and gills by the process of osmosis and then they urinate a much more dilute mixture to get rid of all that excess water.
Saltwater fishes are quite different as the concentration of salt in their blood and tissues is lower than the water surrounding them. Their challenge is to avoid losing water and to keep the excess salt out.
These fishes often drink water through their mouths to keep hydrated. Their kidneys remove salt and conserve water while the salt cells in their gills pump salt into the water.
Using these different methods, Saltwater and freshwater fishes are equally hydrated and salty.
Fishes do actively take in water, but do they get thirsty? Probably not. The reason is that taking in water is more like a reflex action that occurs without requiring a conscious decision on their part (unlike humans), it happens automatically. It is like how we pull our hands away immediately after touching something hot.